Did you maybe test the checkout with the original files, then delete them and create them again and test again with out closing the browser?
if you tested again without closing the browser, it would be remembering the session created from the original checkout pages.
I don't see where the WASF_CheckoutWizard_Compact_Default session is being created in the pages you attached.
I would need you to upload to the server in order to troubleshoot further.